Factorial ANOVA: Simple Effects
Behavior is determined by many factors. Do the
factors interact in their effects on a dependent variable? A researcher is interested
in studying the effect of group psychotherapy and
medication on
depression.
Independent Variables and dependent Variable
1. Independent Variables (Factors)
There are two
factors: the Psychotherapy factor with two levels (psychotherapy and no
psychotherapy) and the Medication factor with three levels (placebo,
low dose and high dose).
It is a 2-by-3 factorial.
Notice that there are six combinations.
|
|
Placebo 1
|
Low Dose 2 |
High Dose 3 |
|
Psychotherapy
1 |
Combination A |
Combination B |
Combination C |
|
No Psychotherapy
2 |
Combination D |
Combination E |
Combination F |
Thirty patients participated in the study.
Use different subjects for all conditions of the experiment.
Since the data are from independent
samples, the factors are between-subjects.
2.
Dependent Variable: Depression scores
After the treatments were
completed, the depression level of each subject was assessed. Higher scores
indicate higher levels of depression.
|
|
Placebo 1
|
Low Dose 2 |
High Dose 3 |
|
Psychotherapy
1
|
4
3
4
3
3 |
1
1
1
1
2 |
2
3
2
2
2 |
|
No
Psychotherapy
2 |
5
5
5
4
5 |
3
4
4
4
3 |
3
2
3
3
2 |
There are two factors (Psychotherapy and Drug). Is there a significant interaction
on depression scores between psychotherapy and medication?
I. Test the Interaction Effect
SPSS for Windows
A.
Enter data.
Create three variables: psy,
drug
and score.
In the "Variable View" window, you will find a column called
"Values". Click on the cell (None) and click on the small grey button to define
the values. Assign descriptive labels to values: For the variable "psy",
assign 1 for Psychotherapy and 2 for No Psychotherapy.
For the variable "drug", assign 1 for Placebo, 2 for Low Dose, and 3 for High
Dose.
The scores in the combination A cell (1,
1) are [4 3 4 3 3].
The scores in the combination B cell (1,
2) are [1 1 1 1 2].
The scores in the combination C cell (1,
3) are [2 3 2 2 2].
The scores in the combination D cell (2,
1) are [5 5 5 4 5].
The scores in the combination E cell (2,
2) are [3 4 4 4 3].
The scores in the combination F cell (2,
3) are [3 2 3 3 2].
B.
From the menus choose: Analyze \ General Linear Model \
Univariate.
1. Select the dependent variable: score. Select the fixed
factors: psy and drug.
2. Click the Options button. Move the two factors (psy and
drug) and the interaction term (psy*drug) to the Display Means for box. In the
Display area, select Descriptive statistics and Homogeneity tests. Click
Continue and OK.
SPSS Printout
A. Examine the ANOVA Table
Begin the interpretation of the results from a two-factor design by starting
with the interaction (Psy By Drug). Was there a significant interaction between
the drug and the psychotherapy factors at the .05 level?
Yes, there was a significant interaction between the drug and the psychotherapy
factors, F(2, 24)= 10, p = .001.
II. Test the Simple Effects of the Psychotherapy Factor
A simple effects test is generally done after a statistically significant
interaction test. The computation involves analyzing
the
effect of one factor at each level of the other factor.
Research Question: Does the effect of the Psychotherapy factor depend on
different levels of the Drug factor? There are three simple effects to be performed.
[1] Does the manipulation of the Psychotherapy factor have a significant
effect on depression scores with the placebo group?
|
|
Placebo 1
|
Low Dose 2
|
High Dose 3
|
|
Psychotherapy (1)
|
3.4
|
1.2
|
2.2
|
|
No Psychotherapy (2) |
4.8
|
3.6
|
2.6
|
[2] Does the manipulation of the Psychotherapy factor have a significant effect
on depression scores with the group receiving the low dose treatment?
|
|
Placebo 1
|
Low Dose 2
|
High Dose 3
|
|
Psychotherapy (1)
|
3.4
|
1.2
|
2.2
|
|
No Psychotherapy (2) |
4.8
|
3.6
|
2.6
|
[3] Does the manipulation of the Psychotherapy factor have a significant effect
on depression scores with the group receiving the high dose treatment?
|
|
Placebo 1
|
Low Dose 2
|
High Dose 3
|
|
Psychotherapy (1)
|
3.4
|
1.2
|
2.2
|
|
No Psychotherapy (2) |
4.8
|
3.6
|
2.6
|
SPSS for Windows
How to Obtain the simple effects
A. From the menus choose:
File
New
Syntax
The Syntax window appears.
B. Copy the following commands and paste it to the Syntax window.
MANOVA
SCORE BY PSY(1 2) DRUG(1 3)
/METHOD= UNIQUE
/ERROR WITHIN
/DESIGN=PSY WITHIN DRUG(1) PSY WITHIN DRUG(2) PSY WITHIN DRUG(3).
Method
Specify the method for partitioning the sums of squares.
Using the regression method (UNIQUE), each
term is corrected for every other term in the model. This is the default. Note
that when there are an equal number of subjects in each cell in a factorial
design, all the methods for partitioning the sums of squares (e.g., regression
method and hierarchical methods) yield the same result.
Design
Simple effects of the factor Psychotherapy for
each level of the Drug factor: Psy Within
Drug (1), Psy Within Drug (2), and Psy Within Drug (3). Note that the number
specified after a WITHIN factor refers to the level of that factor.
C. From the menus choose:
Run
All
SPSS Printout
There are three simple effects tested for the factor Psy.
(1) the effect of the Psychotherapy
factor for individuals within the placebo condition
(2) the effect of the Psychotherapy
factor for individuals within the low dose condition
(3) the effect of the Psychotherapy
factor for individuals within the high dose condition
Output
Note that an observed significant level of .000 is reported as p < .001.
Report the Results
The psychotherapy by drug interaction effect was analyzed using a simple main
effects analysis. Group psychotherapy influenced depression scores for subjects
in the placebo condition, F(1, 24)= 19.60, p <
.001, and the low dose treatment, F(1, 24)= 57.60, p
< .001. However, group psychotherapy did not influence depression scores for
subjects in the high dose treatment, F(1, 24) = 1.60, p
= .218.
Optional Readings
1. Simple Effects Test Following a Significant Interaction by Jason Newsom
2.
Simple Effects, Simple Contrasts, and Main Effect Contrasts by Jason Newsom